Scheduling County Cricket

I subscribe to The Cricketer, a glossy cricket magazine published in England. My copy arrives in Indiana by way of Budapest after about two months transit time. But it’s worth waiting for. In the last issue I received, there’s an interesting tournament design problem relating to the scheduling of round robins.

Here’s a small extract from a Cricketer article by Wasim Kahn, the head of county cricket for Leicestershire:

The idea behind the seeding system was that when you have an asymmetrical system such as 10 teams and 14 matches, if you are at the top end, you might not play some of the other top teams, and others will. There needed to be a fairer, robust seeding system. They are using experts who do this at top-level sport, so everybody buys into that. [The Cricketer, v. 16, no. 4, p. 13.]

Who are these experts? Apparently there’s a cadre of tourneygeeks in England who command universal respect. I’m in the wrong country. But wait. On the same spread there’s another article by BBC cricket expert David Townsend:

Now I have no problem with the invention of a ‘science’ that enables the thick but athletic sons and daughters of middle-class parents to accumulate as much student debt as their peers, but not when it comes to messing with the cricket season. [Ibid p. 12].

So maybe the tourneygeeks are not so universally respected, but at least they’re acknowledged to exist.

I’m a little hurt that the England and Wales Cricket Board did not seek me out for my expert advice. But I’m not one to hold a grudge, so I’ll solve their problem for them anyway. What’s a special relationship for if I can’t reach out across “the pond” to come to the aid of my thick but athletic colleagues.

Here’s the problem. Cricket is a Summer game, and the English Summer simply isn’t long enough to accommodate all of the cricket that people want to play. Back in the day, there was enough time, but that’s before the ECB decided that it really needed to run a full season for each of the three forms of the game.

Now there are 18 counties that play first class cricket. For many years, these were split into two divisions of nine teams each. There were 18 rounds in the championship, so the season could be run on a scrupulously fair pattern, with each team playing each other team twice, once at home, and once away, and drawing two byes.

But starting in 2017, the ECB decided that there was only time enough for fourteen rounds of first class cricket if there was also going to be time to play both T20 cricket and one-day cricket. The top division was limited to eight teams, so that it could continue to play a full double round robin. But the lower division, with ten teams and only the same 14 rounds would have to settle for less than a complete round robin.

But people are unhappy. Some of the teams that have fallen out of the top flight are old stalwarts of English County Cricket like Middlesex, who play their home matches at Lord’s (FN1). The powers that be want to expand the top division to ten teams, shrinking the second division to eight. And, while they’ve had a couple of years to work out how truncate the round robin for the ten-team division, they’re only worrying about it being really fair now that it’s the best teams that might suffer an inequity.

So, how do you decide which four rounds of the double round robin should get the axe?

The trick is not to include, in the second set of pairings, any in which the seeds are both even or both odd. Thus, seed 1 will have repeat fixtures against 2, 4, 6, 8, and 10, but not against 3, 5, 7, or 9. Seed 2 gets a second chance at 1, 3, 5, 7, and 9, but not at 4, 6, 8, or 10. And so forth.

Here’s how it works out. Start with a single, full round robin of the ten teams:

Since you want every team to play every other team at least once, you can use these nine sets of pairings directly. Now you need to generate another five rounds.

Start with the same nine rounds, but this time mark every match in which the seed numbers are both even or both odd:

These are the matches you don’t want. Reassemble the bits left over into five new rounds, which will be added to the first nine to make the full, 14-round schedule:

The point is that observing the even/odd rule means that the repeated matches will be distributed as evenly as possible through the seeds. It’s true that odd-numbered seeds have a small advantage. They always, for example, get to play the worst seed twice and never have to play the best seed twice. But absolute equality is not possible.

That’s it. I hope it helps.

We’re worried about you, over here – worried that about the time balls start crashing into stumps this year Britain will also be crashing out of the European Union.

On the bright side, if that happens my copy of The Cricketer may not be routed through Budapest.

FN1: Lord’s is probably the most iconic cricket ground in England. It is so named not because it is frequented by male peers, but because it was originally developed by a man named “Lord”. Still, it is frequented by peers, and perhaps the name makes them feel a little more at home there.

Among the 18 counties there were 9 votes for a more American style system with conferences and a playoff, and 9 votes for the traditional setup of two divisions with promotion and relegation between the two. In the end the traditionalists proved more intransigent, and got their way.

Almost every full-season minor league is one of these sizes, so it plays really nicely.
14- and 22-game season have similar amounts of “compositeness” in non-baseball schedules.
The AFL has used a 22-game season since the era of the 12-team league.

In order to instill long-term Fairness, (both A and B), the pairings would have to rotate each year, like the NBA does for its Inter-Division matchups:

Each side faces 3 sides at their own grounds only, 3 sides at the other’s grounds only, and 3 sides home-and-home. As an example: in Year 1, side A would Host Sides C, F, and G, Travel to Sides E, I, and J, and have a Home-And-Home with Sides B, D, and H. In Year 2, Sides C, F, and G get the double-rounds, while E, I, and J get them in Year 3.

This leads to a total of 12 Matches per year. It’s also Balanced over the course of 3 years, barring the effects of Relegation, but is somewhat imbalanced in any given year.

So what do we do with the last 2 rounds? Well, since this the Top Flight that we’re talking about now, we may as well use those last 2 rounds as a Playoff for the Title, as well as a Playoff for Relegation. Yes, this goes against Proper English Tradition, but so does having an unbalanced schedule in the first place.

The Top 4 could have Matches 13 & 14 be the first 2 Rounds of a Page Playoff, with the Finals being in an extra Round. Conversely, the Bottom 4 would face off in a Reverse Page Playoff with the final round removed: The loser of the 9th vs 10th Match is Relegated and does not play in Match 14. The winner of that Match faces off against the loser of the 7th vs 8th Match with the loser taking the 2nd Relegation spot. 5th & 6th Place also play-on, with the winner of their match in Week 13 facing off against the loser of the 3 vs 4 round of the Playoff, and the loser of 5 vs 6 facing the winner of 7 vs 8.

Now, if they were keeping the Top Flight at 8 sides, leaving the Bottom with 10, I would split the bottom by Region (rebalancing the regions as needed) with one Full Round-Robin among all teams and a second Region-only Round Robin, with Match 14 being an inter-region match between the side with the same rank as yours; the side that hosts belonging to the Region that hosted only 2 of the 5 regular-season cross-over rounds. The match between the Top Place in each Region would determine the Lower-Division Championship as well as the first Promotion. The loser of that match would have to face the winner of the 2nd Place Match in a 15th Match on a Neutral Ground to determine the 2nd Promotion. The 5th Place match would be for the Wooden Spoon (heh) and the 3rd & 4th Place matches would be just to even out the schedule.